Stationary Anonymous Sequential Games with Undiscounted Rewards

Area of Science:

• Game Theory
• Mathematical Economics
• Computational Game Theory

Background:

• Stationary anonymous sequential games with undiscounted rewards merge infinite-player population games and stochastic games.
• Existing theory primarily addresses specific reward structures.

Purpose of the Study:

• Extend the theoretical framework for stationary anonymous sequential games.
• Analyze both total expected reward and expected average reward scenarios.
• Establish the relationship between infinite and finite player game equilibria.

Main Methods:

• Theoretical extension of game theory models.
• Analysis of limit behavior as player populations approach infinity.
• Comparative analysis of finite and infinite player game equilibria.

Main Results:

• Demonstrated that equilibria in infinite-player anonymous sequential games are limits of finite-player game equilibria.
• Successfully extended the theory to encompass total expected reward and expected average reward.

Conclusions:

• The study provides a robust theoretical foundation for analyzing large-scale anonymous sequential games.
• Findings offer insights into the convergence of strategies in games with growing player numbers.
• The results are illustrated with practical examples.